OpenRaiser/Intern-Atlas huggingface dataset:
On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem
Venue: arXiv cs.NA 2008
Year: 2008

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions.
Approximating Multi-Criteria Max-TSP
Venue: arXiv cs.DS 2008
Year: 2008

We present randomized approximation algorithms for multi-criteria Max-TSP. For Max-STSP with k > 1 objective functions, we obtain an approximation ratio of $1/k - \eps$ for arbitrarily small $\eps > 0$. For Max-ATSP with k objective functions, we obtain an approximation ratio of $1/(k+1) - \eps$.
On the d-dimensional Quasi-Equally Spaced Sampling
Venue: arXiv cs.IT 2008
Year: 2008

We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited signal. We focus on the case where the random variables characterizing these matrices are d-dimensional vectors, independent, and quasi-equally spaced, i.e., they have an arbitrary distribution and their averages are vertices of a d-dimensional grid. Although a closed form expression of the eigenvalue distribution is still unknown, under these conditions we are able (i) to derive the distribution moments as the matrix size grows to infinity, while its aspect ratio is kept constant, and (ii) to show that the eigenvalue distribution tends to the Marcenko-Pastur law as d->infinity. These results can find application in several fields, as an example we show how they can be used for the estimation of the mean square error provided by linear reconstruction techniques.
Conceptualization of seeded region growing by pixels aggregation. Part 4: Simple, generic and robust extraction of grains in granular materials obtained by X-ray tomography
Venue: arXiv cs.CV 2008
Year: 2008

This paper proposes a simple, generic and robust method to extract the grains from experimental tridimensionnal images of granular materials obtained by X-ray tomography. This extraction has two steps: segmentation and splitting. For the segmentation step, if there is a sufficient contrast between the different components, a classical threshold procedure followed by a succession of morphological filters can be applied. If not, and if the boundary needs to be localized precisely, a watershed transformation controlled by labels is applied. The basement of this transformation is to localize a label included in the component and another label in the component complementary. A "soft" threshold following by an opening is applied on the initial image to localize a label in a component. For any segmentation procedure, the visualisation shows a problem: some groups of two grains, close one to each other, become connected. So if a classical cluster procedure is applied on the segmented binary image, these numerical connected grains are considered as a single grain. To overcome this problem, we applied a procedure introduced by L. Vincent in 1993. This grains extraction is tested for various complexes porous media and granular material, to predict various properties (diffusion, electrical conductivity, deformation field) in a good agreement with experiment data.
A stabilized finite element formulation for advection-diffusion using the generalized finite element framework
Venue: arXiv cs.NA 2008
Year: 2008

The following work presents a generalized (extended) finite element formulation for the advection-diffusion equation. Using enrichment functions that represent the exponential nature of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Peclet numbers (up to Pe = 25) in one and two-dimensions. As opposed to traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with an enrichment function. To contextualize this method among other stabilized methods, we show by decomposition of the solution (in a multiscale manner) an equivalence to both Galerkin/least-squares type methods and those that use bubble functions. This work also presents a strategy for constructing the enrichment function for problems with complex geometries by employing a global-local approach.
Problems of robustness for universal coding schemes
Venue: arXiv cs.IT 2008
Year: 2008

The Lempel-Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robustness of this property under small violations of ergodicity is studied. A notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compressing schemes from a large class are non-robust in the following sense: if the randomness deficiency grows arbitrarily slowly on initial fragments of an infinite sequence then the property of asymptotic optimality of any universal compressing algorithm can be violated. Lempel-Ziv compressing algorithms are robust on infinite sequences generated by ergodic Markov chains when the randomness deficiency of its initial fragments of length $n$ grows as $o(n)$.
A Fixed-Parameter Algorithm for Random Instances of Weighted d-CNF Satisfiability
Venue: arXiv cs.DS 2008
Year: 2008

We study random instances of the weighted $d$-CNF satisfiability problem (WEIGHTED $d$-SAT), a generic W[1]-complete problem. A random instance of the problem consists of a fixed parameter $k$ and a random $d$-CNF formula $\weicnf{n}{p}{k, d}$ generated as follows: for each subset of $d$ variables and with probability $p$, a clause over the $d$ variables is selected uniformly at random from among the $2^d - 1$ clauses that contain at least one negated literals. We show that random instances of WEIGHTED $d$-SAT can be solved in $O(k^2n + n^{O(1)})$-time with high probability, indicating that typical instances of WEIGHTED $d$-SAT under this instance distribution are fixed-parameter tractable. The result also hold for random instances from the model $\weicnf{n}{p}{k,d}(d')$ where clauses containing less than $d' (1 < d' < d)$ negated literals are forbidden, and for random instances of the renormalized (miniaturized) version of WEIGHTED $d$-SAT in certain range of the random model's parameter $p(n)$. This, together with our previous results on the threshold behavior and the resolution complexity of unsatisfiable instances of $\weicnf{n}{p}{k, d}$, provides an almost complete characterization of the typical-case behavior of random instances of WEIGHTED $d$-SAT.
Overlaid Cellular and Mobile Ad Hoc Networks
Venue: arXiv cs.IT 2008
Year: 2008

In cellular systems using frequency division duplex, growing Internet services cause unbalance of uplink and downlink traffic, resulting in poor uplink spectrum utilization. Addressing this issue, this paper considers overlaying an ad hoc network onto a cellular uplink network for improving spectrum utilization and spatial reuse efficiency. Transmission capacities of the overlaid networks are analyzed, which are defined as the maximum densities of the ad hoc nodes and mobile users under an outage constraint. Using tools from stochastic geometry, the capacity tradeoff curves for the overlaid networks are shown to be linear. Deploying overlaid networks based on frequency separation is proved to achieve higher network capacities than that based on spatial separation. Furthermore, spatial diversity is shown to enhance network capacities.
Challenging More Updates: Towards Anonymous Re-publication of Fully Dynamic Datasets
Venue: arXiv cs.DB 2008
Year: 2008

Most existing anonymization work has been done on static datasets, which have no update and need only one-time publication. Recent studies consider anonymizing dynamic datasets with external updates: the datasets are updated with record insertions and/or deletions. This paper addresses a new problem: anonymous re-publication of datasets with internal updates, where the attribute values of each record are dynamically updated. This is an important and challenging problem for attribute values of records are updating frequently in practice and existing methods are unable to deal with such a situation. We initiate a formal study of anonymous re-publication of dynamic datasets with internal updates, and show the invalidation of existing methods. We introduce theoretical definition and analysis of dynamic datasets, and present a general privacy disclosure framework that is applicable to all anonymous re-publication problems. We propose a new counterfeited generalization principle alled m-Distinct to effectively anonymize datasets with both external updates and internal updates. We also develop an algorithm to generalize datasets to meet m-Distinct. The experiments conducted on real-world data demonstrate the effectiveness of the proposed solution.
Malleable Coding: Compressed Palimpsests
Venue: arXiv cs.IT 2008
Year: 2008

A malleable coding scheme considers not only compression efficiency but also the ease of alteration, thus encouraging some form of recycling of an old compressed version in the formation of a new one. Malleability cost is the difficulty of synchronizing compressed versions, and malleable codes are of particular interest when representing information and modifying the representation are both expensive. We examine the trade-off between compression efficiency and malleability cost under a malleability metric defined with respect to a string edit distance. This problem introduces a metric topology to the compressed domain. We characterize the achievable rates and malleability as the solution of a subgraph isomorphism problem. This can be used to argue that allowing conditional entropy of the edited message given the original message to grow linearly with block length creates an exponential increase in code length.
On the Multiplexing Gain of K-user Partially Connected Interference Channel
Venue: arXiv cs.IT 2008
Year: 2008

The multiplexing gain (MUXG) of $K$-user interference channel (IC) with partially connected interfering links is analyzed. The motivation for the partially connected IC comes from the fact that not all interferences are equally strong in practice. The MUXG is characterized as a function of the number ($K$) of users and the number ($N \geq 1$) of interfering links. Our analysis is mainly based on the interference alignment (IA) technique to mitigate interference. Our main results are as follows: One may expect that higher MUXG can be attained when some of interfering links do not exist. However, when $N$ is odd and $K=N+2$, the MUXG is not increased beyond the optimal MUXG of fully connected IC, which is $\frac{KM}{2}$. The number of interfering links has no influence on the achievable MUXG using IA, but affects the efficiency in terms of the number of required channel realizations: When N=1 or 2, the optimal MUXG of the fully connected IC is achievable with a finite number of channel realizations. In case of $N \geq 3$, however, the MUXG of $\frac{KM}{2}$ can be achieved asymptotically as the number of channel realizations tends to infinity.
Increase of Software Safety
Venue: arXiv cs.SE 2008
Year: 2008

New model of software safety is offered. Distribution of mistakes in program on stages of life cycle is researched. Study of ways of increase of reliability of software at help simulation program is leaded.
Linear-Programming Receivers
Venue: arXiv cs.IT 2008
Year: 2008

It is shown that any communication system which admits a sum-product (SP) receiver also admits a corresponding linear-programming (LP) receiver. The two receivers have a relationship defined by the local structure of the underlying graphical model, and are inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This concept is a generalization of the concept of 'pseudocodewords' for linear codes. It is proved that the LP receiver has the 'optimum certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. While the LP receiver is generally more complex than the corresponding SP receiver, the LP receiver and its associated pseudoconfiguration structure provide an analytic tool for the analysis of SP receivers. As an example application, we show how the LP design technique may be applied to the problem of joint equalization and decoding.
Algorithmic Problem Complexity
Venue: arXiv cs.CC 2008
Year: 2008

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at determination of computer abilities in solving different problems and estimation of resources that computers need to do this. Here we build the part of this theory related to static measures of algorithms. At first, we consider problems for finite words and study algorithmic complexity of such problems, building optimal complexity measures. Then we consider problems for such infinite objects as functions and study algorithmic complexity of these problems, also building optimal complexity measures. In the second part of the work, complexity of algorithmic problems, such as the halting problem for Turing machines, is measured by the classes of automata that are necessary to solve this problem. To classify different problems with respect to their complexity, inductive Turing machines, which extend possibilities of Turing machines, are used. A hierarchy of inductive Turing machines generates an inductive hierarchy of algorithmic problems. Here we specifically consider algorithmic problems related to Turing machines and inductive Turing machines, and find a place for these problems in the inductive hierarchy of algorithmic problems.
On Cycles in AS Relationships
Venue: arXiv cs.NI 2008
Year: 2008

Several users of our AS relationship inference data (http://www.caida.org/data/active/as-relationships/), released with cs/0604017, asked us why it contained AS relationship cycles, e.g., cases where AS A is a provider of AS B, B is a provider of C, and C is a provider of A, or other cycle types. Having been answering these questions in private communications, we have eventually decided to write down our answers here for future reference.
Algorithms for Secretary Problems on Graphs and Hypergraphs
Venue: arXiv cs.DS 2008
Year: 2008

We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following secretary problem: Initially given R, and the size of L, the algorithm receives the vertices of L sequentially, in a random order. When a vertex l \in L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R, or decide that l will remain unmatched. Dimitrov and Plaxton show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l \in L, the weights on all edges incident to l are identical.) We use a similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Perhaps of more interest is the fact that our analysis is easily extended to obtain competitive algorithms for similar problems, such as to find disjoint sets of edges in hypergraphs where edges arrive online. We also introduce secretary problems with adversarially chosen groups. Finally, we give a 2e-competitive algorithm for the secretary problem on graphic matroids, where, with edges appearing online, the goal is to find a maximum-weight acyclic subgraph of a given graph.
CSI: A Paradigm for Behavior-oriented Delivery Services in Mobile Human Networks
Venue: arXiv cs.NI 2008
Year: 2008

We propose behavior-oriented services as a new paradigm of communication in mobile human networks. Our study is motivated by the tight user-network coupling in future mobile societies. In such a paradigm, messages are sent to inferred behavioral profiles, instead of explicit IDs. Our paper provides a systematic framework in providing such services. First, user behavioral profiles are constructed based on traces collected from two large wireless networks, and their spatio-temporal stability is analyzed. The implicit relationship discovered between mobile users could be utilized to provide a service for message delivery and discovery in various network environments. As an example application, we provide a detailed design of such a service in challenged opportunistic network architecture, named CSI. We provide a fully distributed solution using behavioral profile space gradients and small world structures. Our analysis shows that user behavioral profiles are surprisingly stable, i.e., the similarity of the behavioral profile of a user to its future behavioral profile is above 0.8 for two days and 0.75 for one week, and remains above 0.6 for five weeks. The correlation coefficient of the similarity metrics between a user pair at different time instants is above 0.7 for four days, 0.62 for a week, and remains above 0.5 for two weeks. Leveraging such a stability in user behaviors, the CSI service achieves delivery rate very close to the delay-optimal strategy (above 94%), with minimal overhead (less than 84% of the optimal). We believe that this new paradigm will act as an enabler of multiple new services in mobile societies, and is potentially applicable in server-based, heterogeneous or infrastructure-less wireless environments.
Optimal Direct Sum and Privacy Trade-off Results for Quantum and Classical Communication Complexity
Venue: arXiv cs.DC 2008
Year: 2008

We show optimal Direct Sum result for the one-way entanglement-assisted quantum communication complexity for any relation f subset of X x Y x Z. We show: Q^{1,pub}(f^m) = Omega(m Q^{1,pub}(f)), where Q^{1,pub}(f), represents the one-way entanglement-assisted quantum communication complexity of f with error at most 1/3 and f^m represents m-copies of f. Similarly for the one-way public-coin classical communication complexity we show: R^{1,pub}(f^m) = Omega(m R^{1,pub}(f)), where R^{1,pub}(f), represents the one-way public-coin classical communication complexity of f with error at most 1/3. We show similar optimal Direct Sum results for the Simultaneous Message Passing quantum and classical models. For two-way protocols we present optimal Privacy Trade-off results leading to a Weak Direct Sum result for such protocols. We show our Direct Sum and Privacy Trade-off results via message compression arguments which also imply a new round elimination lemma in quantum communication. This allows us to extend classical lower bounds on the cell probe complexity of some data structure problems, e.g. Approximate Nearest Neighbor Searching on the Hamming cube {0,1}^n and Predecessor Search to the quantum setting. In a separate result we show that Newman's technique of reducing the number of public-coins in a classical protocol cannot be lifted to the quantum setting. We do this by defining a general notion of black-box reduction of prior entanglement that subsumes Newman's technique. We prove that such a black-box reduction is impossible for quantum protocols. In the final result in the theme of message compression, we provide an upper bound on the problem of Exact Remote State Preparation.
General Auction Mechanism for Search Advertising
Venue: arXiv cs.GT 2008
Year: 2008

In sponsored search, a number of advertising slots is available on a search results page, and have to be allocated among a set of advertisers competing to display an ad on the page. This gives rise to a bipartite matching market that is typically cleared by the way of an automated auction. Several auction mechanisms have been proposed, with variants of the Generalized Second Price (GSP) being widely used in practice. A rich body of work on bipartite matching markets builds upon the stable marriage model of Gale and Shapley and the assignment model of Shapley and Shubik. We apply insights from this line of research into the structure of stable outcomes and their incentive properties to advertising auctions. We model advertising auctions in terms of an assignment model with linear utilities, extended with bidder and item specific maximum and minimum prices. Auction mechanisms like the commonly used GSP or the well-known Vickrey-Clarke-Groves (VCG) are interpreted as simply computing a \emph{bidder-optimal stable matching} in this model, for a suitably defined set of bidder preferences. In our model, the existence of a stable matching is guaranteed, and under a non-degeneracy assumption a bidder-optimal stable matching exists as well. We give an algorithm to find such matching in polynomial time, and use it to design truthful mechanism that generalizes GSP, is truthful for profit-maximizing bidders, implements features like bidder-specific minimum prices and position-specific bids, and works for rich mixtures of bidders and preferences.
Simulations of Large-scale WiFi-based Wireless Networks: Interdisciplinary Challenges and Applications
Venue: arXiv cs.CE 2008
Year: 2008

Wireless Fidelity (WiFi) is the fastest growing wireless technology to date. In addition to providing wire-free connectivity to the Internet WiFi technology also enables mobile devices to connect directly to each other and form highly dynamic wireless adhoc networks. Such distributed networks can be used to perform cooperative communication tasks such ad data routing and information dissemination in the absence of a fixed infrastructure. Furthermore, adhoc grids composed of wirelessly networked portable devices are emerging as a new paradigm in grid computing. In this paper we review computational and algorithmic challenges of high-fidelity simulations of such WiFi-based wireless communication and computing networks, including scalable topology maintenance, mobility modelling, parallelisation and synchronisation. We explore similarities and differences between the simulations of these networks and simulations of interacting many-particle systems, such as molecular dynamics (MD) simulations. We show how the cell linked-list algorithm which we have adapted from our MD simulations can be used to greatly improve the computational performance of wireless network simulators in the presence of mobility, and illustrate with an example from our simulation studies of worm attacks on mobile wireless adhoc networks.